What is the horse power of a 240-V squirrel-cage induction motor that is measuring 50 amps per line with a clamp meter. The power factor is 0.90 and the full-load efficiency is 92%.

To calculate the horsepower (HP) of the squirrel-cage induction motor, we can use the following steps:

### Step 1: Calculate the Input Power in Watts
The formula for electrical power \( P_{\text{in}} \) in a three-phase system is:

\[
P_{\text{in}} = \sqrt{3} \times V \times I \times \text{PF}
\]

Where:
- \( V \) = Line voltage (240 V)
- \( I \) = Line current (50 A)
- \( \text{PF} \) = Power factor (0.90)
- \( \sqrt{3} \) = 1.732 (constant for three-phase systems)

Substitute the given values:

\[
P_{\text{in}} = 1.732 \times 240 \times 50 \times 0.90 = 18,719.04 \text{ watts}
\]

### Step 2: Calculate the Output Power
The output power \( P_{\text{out}} \) of the motor is the input power multiplied by the efficiency \( \eta \):

\[
P_{\text{out}} = P_{\text{in}} \times \eta
\]

Where \( \eta \) is the efficiency (92% or 0.92):

\[
P_{\text{out}} = 18,719.04 \times 0.92 = 17,212.91 \text{ watts}
\]

### Step 3: Convert Watts to Horsepower
To convert the power from watts to horsepower, we use the conversion factor \( 1 \, \text{HP} = 746 \, \text{watts} \):

\[
\text{HP} = \frac{P_{\text{out}}}{746} = \frac{17,212.91}{746} \approx 23.07 \, \text{HP}
\]

### Final Answer:
The horsepower of the motor is approximately **23.07 HP**.

Would you like more details or have any further questions?

Here are some related questions you might find useful:
1. What is the significance of the power factor in electric motors?
2. How does the efficiency of a motor affect its performance?
3. What are other methods to calculate motor horsepower?
4. How does three-phase power differ from single-phase power?
5. What are typical values for power factor in industrial motors?

**Tip:** A lower power factor means the motor is not using power as efficiently, potentially leading to higher energy costs.

Learn how to calculate the horsepower of a 240V squirrel-cage induction motor, measuring 50 amps, with a power factor of 0.90 and an efficiency of 92%. This step-by-step solution explains the key electrical formulas and concepts involved in calculating motor horsepower in a three-phase system.

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